After Max Planck determined that energy is released and
absorbed by atoms in certain fixed amounts known as quanta,
Albert Einstein took his work a step further, determining that radiant
energy is also quantized—he called the discrete energy packets photons.
Einstein’s theory was that electromagnetic radiation (light, for
example) has characteristics of both a wave and a stream of particles.

The Bohr Model of the Atom

In 1913, Niels Bohr used what had recently been discovered
about energy to propose his planetary model of the atom. In the
Bohr model, the neutrons and protons are contained in a small, dense
nucleus, which the electrons orbit in defined spherical orbits.
He referred to these orbits as “shells” or “energy levels” and designated
each by an integer: 1, 2, 3, etc. An electron occupying the first
energy level was thought to be closer to the nucleus and have lower
energy than one that was in a numerically higher energy level. Bohr
theorized that energy in the form of photons must be absorbed in
order for an electron to move from a lower energy level to a higher
one, and is emitted when an electron travels from a higher energy
level to a lower one. In the Bohr model, the lowest energy state
available for an electron is the ground state, and
all higher-energy states are excited states.

Orbitals and Quantum Numbers

In the 1920s, Werner Heisenberg put forth his uncertainty
principle, which states that, at any one time, it is impossible
to calculate both the momentum and the location of an electron in
an atom; it is only possible to calculate the probability of
finding an electron within a given space. This meant that electrons,
instead of traveling in defined orbits or hard, spherical “shells,”
as Bohr proposed, travel in diffuse clouds around the nucleus.

When we say “orbital,” the image below is what we picture
in our minds.

To describe the location of electrons, we use quantum
numbers. Quantum numbers are basically used to describe certain
aspects of the locations of electrons. For example, the quantum
numbers n, l,
and ml describe
the position of the electron with respect to the nucleus, the shape
of the orbital, and its special orientation, while the quantum number ms describes
the direction of the electron’s spin within a given orbital.

Below are the four quantum numbers, showing how they are
depicted and what aspects of electrons they describe.

Principal quantum number (n)

Has positive values of 1, 2, 3, etc. As n increases,
the orbital becomes larger—this means that the electron has a higher
energy level and is less tightly bound to the nucleus.

Second quantum number or azimuthal quantum
number (l )

Has values from 0 to n – 1.
This defines the shape of the orbital, and the value of l is
designated by the letters s, p, d,
and f, which correspond to values for l of
0, 1, 2, and 3. In other words, if the value of l is
0, it is expressed as s; if l =
1 = p, l = 2 = d,
and l = 3 = f.

Magnetic quantum number (ml)

Determines the orientation of the orbital in
space relative to the other orbitals in the atom. This quantum number
has values from -l through 0 to +l.

Spin quantum number (ms)

Specifies the value for the spin and is either
+1/2 or -1/2. No more than two electrons can occupy any one orbital.
In order for two electrons to occupy the same orbital, they must
have opposite spins.

Orbitals that have the same principal quantum number, n,
are part of the same electron shell. For example, orbitals
that have n = 2 are said to be in the second shell.
When orbitals have the same n and l,
they are in the same subshell; so orbitals that have n =
2 and l = 3 are said to be 2f orbitals,
in the 2f subshell.

Finally, you should keep in mind that according to the Pauli
exclusion principle, no two electrons in an atom
can have the same set of four quantum numbers. This means
no atomic orbital can contain more than two electrons,
and if the orbital does contain two electrons, they must be of opposite
spin.